2017 AMC 10B Problem 8

Question

Points

A(11, 9)

and

B(2, -3)

are vertices of

\triangle ABC

with

AB=AC.

The altitude from

A

meets the opposite side at

D(-1, 3).

What are the coordinates of point

C?

(-8, 9)

(-4, 8)

(-4, 9)

(-2, 3)

(-1, 0)

In an isosceles triangle, the altitude from the vertex also bisects the base

Use

D

as the midpoint of

BC

Since

AB=AC,

the altitude from

A

also bisects the base

BC.

Therefore,

D

is the midpoint of

BC.

If

C=(x,y),

then we have

\frac{x+2}2 = -1,

\frac{y-3}2=3.

As such,

C=(x,y)=(-4,9).

Thus, the correct answer is C .

Problem 8 in other years